A car travels 3km due north then 5 km east. represent these displacement graphically and determine the resultant displace ment
so, did you graph it?
think of the Pythagorean Theorem.
To represent the displacement graphically, we can use a coordinate system. Let's assume the starting point of the car is at the origin, (0,0).
The first step is to travel 3 km due north. Since we are going up, the displacement is in the positive y-direction. Therefore, the first point is (0,3).
The second step is to travel 5 km east. Since we are going to the right, the displacement is in the positive x-direction. Therefore, the second point is (5,3).
To find the resultant displacement, we can use the Pythagorean theorem. The resultant displacement is the hypotenuse of a right triangle formed by the x and y displacements.
Using the Pythagorean theorem, the resultant displacement is √((5^2) + (3^2)) = √(25 + 9) = √34 km.
Therefore, the resultant displacement is approximately 5.83 km.
To represent the displacement graphically, we can use a coordinate system. Let's assume the starting point is the origin (0, 0).
The car travels 3 km due north, which means it moves 3 units upwards on the y-axis. We can represent this displacement as (0, 3).
After that, the car travels 5 km east, which means it moves 5 units to the right on the x-axis. We can represent this displacement as (5, 3).
To determine the resultant displacement, we can use the Pythagorean theorem since the displacements form a right-angled triangle. The Pythagorean theorem states that the square of the hypotenuse (resultant displacement) is equal to the sum of the squares of the other two sides.
Using the displacements we calculated, the length of the hypotenuse (resultant displacement) can be found as follows:
Resultant displacement = √((5)^2 + (3)^2)
= √(25 + 9)
= √34
≈ 5.83 km
So, the resultant displacement is approximately 5.83 km.